Would being uneducated and poor be counted as a character trait?

No, that's backstory.

Charater traits might well by _why_ they are uneducated and poor, though - for instance, a character who is lazy and stupid is likely to end up uneducated, and a character who is careless with money is likely to end up poor.

No, because he/she didn't choose to be born in a poor environment with little education. Plus that's a part of their background and not personality.

These are facts; traits would be how the character deals with these (self-pitying, quick to anger, humble, etc.)

I don't think they are. That's part of their background and though it makes up part of who they are, it is not a trait.